Herman Cain, the former business executive who has emerged as a front-runner in some polls, said he would build an electrified fence on the border with Mexico that could kill people who try to cross illegally. Representative Michele Bachmann of Minnesota vowed to make English the government’s official language, to build a “secure double fence” and to eliminate “taxpayer-funded benefits for illegal aliens.”

Mr. Cain, speaking at a Tea Party-sponsored rally in Tennessee, made some of his most pointed remarks yet on the issue. He said he might use military troops “with real guns and real bullets” to stop intruders.

Responding to anyone who might consider his remarks “insensitive,” Mr. Cain said the real fault lies with some illegal immigrants. “It’s insensitive for them to be killing our citizens, killing our border agents,” he said. “That’s what’s insensitive. And that mess has to stop.”

Deploying equally strong language, Mrs. Bachmann gave one of the great stem-winding speeches of her campaign. She described illegal immigration as an economic as well as a security threat. “This issue cannot be allowed to stand without fighting back,” she said, drawing applause from a crowd of about 60.

It was no coincidence that she spoke in this Iowa community with the same name as Gov. Rick Perry of Texas. The campaign billed the event as “Bachmann Takes it to Perry Rally.”

Mr. Perry stole much heat and light from Mrs. Bachmann after entering the Republican presidential race this summer, but since then he has been damaged when conservative voters learned of some immigration policies he advocated in Texas.

Even as he has fallen back in polls nationally and in Iowa, Mrs. Bachmann has not been the beneficiary — primarily, that has been Mr. Cain.

Mrs. Bachmann’s appeal seemed targeted at voters in Iowa, where her campaign has placed most if its bets ahead of the caucuses early next year.

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In the speech, she attacked the law Mr. Perry signed in 2001 allowing undocumented students who graduate from a Texas high school to attend a state college on in-state tuition. She said it violates a 1996 federal law.

She also cited figures from a conservative group, the Federation for American Immigration Reform, maintaining that illegal immigration costs taxpayers $133 billion a year, most of it spent on education.

This week, some leading conservative evangelical pastors issued an appeal to the Republican candidates to soften their rhetoric and proposals on immigration, warning that the debate was stigmatizing and alienating Hispanics, who have flocked to evangelical churches in recent years. The appeal came from Richard Land of the Southern Baptist Convention; Matthew D. Staver, dean of the law school at Liberty University; and the Rev. Samuel Rodriguez, president of the largest national conference of Hispanic evangelical churches.

Brent A. Wilkes, vice chairman of the National Hispanic Leadership Agenda, said Mr. Cain’s remarks were reflective of increasingly harsh prescriptions offered by the Republican candidates for dealing with illegal immigration.

“These folks who come across the border are at most committing a misdemeanor,” Mr. Wilkes said. “To suggest that they would be electrocuted or shot would be to treat them harsher than we treat murderers or rapists.”

Mrs. Bachmann insisted she was not taking aim at Hispanics. It is a matter of fairness, she said. She pointed to her own family of “honest, hard-working” Norwegian immigrants, who came to Iowa seven generations ago.

“When they came in, they agreed they’d learn our Constitution, they’d live under the laws of Iowa and the United States, they agreed to learn English and to assimilate into their society.”

“It’s high time,” she said, “we stand up again unashamedly” for American values.

Most of the audience applauded. One dissenter who heard her, Eddie Diaz, a resident of Perry, said, “I’m tired of candidates on both sides using scare tactics against illegal immigrants.”

A version of this article appears in print on October 16, 2011, on Page A22 of the New York edition with the headline: At Rallies, 2 Candidates Deliver Blistering Attacks on Illegal Immigration. Order Reprints|Today's Paper|Subscribe